2023/09/13 by Le Chung Tran, Tran, Le
Computer Science · Mathematics · #05E40 #13C15 #13D05 #13F20 #Coding theory and cryptography #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2309.07286
openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we establish initially regular sequences on cycles of the form C3n+2 for n≥ 1, in the sense of \citeFHM-ini. These sequences accurately compute the depth of these cycles, completing the case of finding effective initially regular sequences on cycles. Our approach involves a careful analysis of associated primes of initial ideals of the form \rmini_>(I,f) for arbitrary monomial ideals I and f linear sums. We describe the minimal associated primes of these ideals in terms of the minimal primes of I. Moreover, we obtain a description of the embedded associated primes of arbitrary monomial ideals. Finally, we accurately compute the depth of certain types of unicyclic graphs.